Photonic systems that transmit and process microwave-frequency analog signals have traditionally been encumbered by relatively large signal distortion and noise. Optical phase modulation (PM) and frequency modulation (FM) are promising techniques that can improve system performance. In this dissertation, I discuss an optical filtering approach to demodulation of PM and FM signals, which does not rely on high frequency electronics, and which scales in linearity with increasing photonic integration. I present an analytical model, filter designs and simulations, and experimental results using planar lightwave circuit (PLC) filters and FM distributed Bragg reflector (DBR) lasers. The linearity of the PM and FM photonic links exceed that of the current state-of-the-art.